Prove the following proposition. Proposition: The iterated sequence defined by a₁ = 2 and an = √3an-1 + 4 has a convergent subsequence. Proof. We begin by proving that the sequence (an) is induction bounded We easily see that a₁ = 2 ≤ we have that an = √ +4≤ we therefore conclude that (an) has a 3an-1 contradiction Indeed we prove by Cauchy convergent . Assuming that an-1 ≤ By applying the subsequence. Completeness Axiom Bolzano-Weierstrass Theorem that an S

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